Payal Tandon
Co-founder, e-GMAT
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Question 2

If P and Q are positive integers, is the product 3PQ divisible by 2?

1. 6Q3 + 2 is an even number
2. P + 8Q2 is a prime number

B

Solution

Steps 1 & 2: Understand Question and Draw Inferences

3PQ is divisible by 2, if:

• 3PQ is even

–>  PQ is even (Odd term 3 plays no role in the even-odd nature of product 3PQ)

–>  P is even (Power doesn’t impact the even-odd nature of a term)

So, to answer the question we need to find if P is even

Step 3: Analyze Statement 1

6Q3 + 2 is an even number

Not Sufficient. We do not know if P is even or odd

Step 4: Analyze Statement 2

P + 8Q2 is a prime number

All the prime numbers except 2 are odd

–>  As Q ≠0, P + 8Q2> 2      (Given: Q is a positive integer => Q >0)

–>  P + 8Q2 is always odd

8Q2 is always even

–>  P must be odd                                                                                  (Odd + Even = Odd)

Sufficient.

Step 5: Analyze Both Statements Together (if needed)

We get a unique answer in step 4, so this step is not required